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Kernel Measures of Conditional Dependence
We propose a new measure of conditional dependence of random variables, based on normalized cross-covariance operators on reproducing kernel Hilbert spaces. Unlike previous kernel dependence measures, the proposed criterion does not depend on the choice of kernel in the limit of infinite data, for a wide class of kernels. At the same time, it has a straightforward empirical estimate with good convergence behaviour. We discuss the theoretical properties of the measure, and demonstrate its application in experiments.
@inproceedings{4914, title = {Kernel Measures of Conditional Dependence}, journal = {Advances in Neural Information Processing Systems 20: 21st Annual Conference on Neural Information Processing Systems 2007}, booktitle = {Advances in neural information processing systems 20}, abstract = {We propose a new measure of conditional dependence of random variables, based on normalized cross-covariance operators on reproducing kernel Hilbert spaces. Unlike previous kernel dependence measures, the proposed criterion does not depend on the choice of kernel in the limit of infinite data, for a wide class of kernels. At the same time, it has a straightforward empirical estimate with good convergence behaviour. We discuss the theoretical properties of the measure, and demonstrate its application in experiments.}, pages = {489-496}, editors = {JC Platt and D Koller and Y Singer and S Roweis}, publisher = {Curran}, organization = {Max-Planck-Gesellschaft}, school = {Biologische Kybernetik}, address = {Red Hook, NY, USA}, month = sep, year = {2008}, slug = {4914}, author = {Fukumizu, K. and Gretton, A. and Sun, X. and Sch{\"o}lkopf, B.}, month_numeric = {9} }